Learn English – Hard to breath or difficulty breathing

Yes, the OP's question is correct grammatically; it conveys the same sense as the second question.

Has someone ever hit you on the nose?

This sentence is in the active voice. It can be changed into the passive as follows:

Have you ever been hit on the nose by someone?

If you want to be informal in your conversation or writing, you can use 'get' instead of 'be' to form the passive as follows:

Have you ever gotten hit on the nose by someone?

No, you cannot say 'have difficulty to do something'. 'have difficulty (in) doing something' will do instead. I've just checked the oxford dictionary again. You are right.